Evolution-EM signals before earthquakes in terms of mesomechanics and complexity

MHz-to-kHz electromagnetic (EM) anomalies have been detected worldwide over time intervals ranging from a few days to a few hours prior to near-surface earthquakes (EQs) that have occurred on land with magnitude approximately six or larger. The MHz radiation systematically appears earlier than the kHz. Laboratory experiments on rock samples reveal a similar change in the frequency content during progressive deformation, i.e. the emissions exhibit a frequency shift from MHz to kHz just before failure of the samples. Herein, we attempt to associate these consecutively emerging MHz and kHz modes of the pre-fracture EM emission with successive distinct stages of the fracture preparation process and the associated fracture mechanisms. We base our approach on synergetic principles of physical mesomechanics. A universal principle of physical mesomechanics is that the plastic deformation of a solid is related to its loss of shear stability at the micro-, meso-, and macroscale levels. Global fracture is determined by the mechanism controlling the development of macroscale bands of localized deformation associated with meso- and microscale relaxation processes. The major result we obtain is that the shift from MHz to kHz EM activity may signal the transition of plastic flow localization from the mesoscale to the macroscale, culminating in global fracture. A complexity measure (Approximate Entropy) and a persistency–anti-persistency measure (Hurst exponent) also give evidence of a two stage-model of EQ preparation process: significant complexity decrease and accession of persistency can be confirmed in the strong kHz EM activity that emerges in the tail of the pre-seismic EM activity. Laboratory experiments on rock samples reveal similar symptoms of an imminent global instability.     

Linear Elastic and Cohesive Fracture Analysis to Model Hydraulic Fracture in Brittle and Ductile Rocks

Hydraulic fracturing technology is being widely used within the oil and gas industry for both waste injection and unconventional gas production wells. It is essential to predict the behavior of hydraulic fractures accurately based on understanding the fundamental mechanism(s). The prevailing approach for hydraulic fracture modeling continues to rely on computational methods based on Linear Elastic Fracture Mechanics (LEFM). Generally, these methods give reasonable predictions for hard rock hydraulic fracture processes, but still have inherent limitations, especially when fluid injection is performed in soft rock/sand or other non-conventional formations. These methods typically give very conservative predictions on fracture geometry and inaccurate estimation of required fracture pressure. One of the reasons the LEFM-based methods fail to give accurate predictions for these materials is that the fracture process zone ahead of the crack tip and softening effect should not be neglected in ductile rock fracture analysis. A 3D pore pressure cohesive zone model has been developed and applied to predict hydraulic fracturing under fluid injection. The cohesive zone method is a numerical tool developed to model crack initiation and growth in quasi-brittle materials considering the material softening effect. The pore pressure cohesive zone model has been applied to investigate the hydraulic fracture with different rock properties. The hydraulic fracture predictions of a three-layer water injection case have been compared using the pore pressure cohesive zone model with revised parameters, LEFM-based pseudo 3D model, a Perkins-Kern–Nordgren (PKN) model, and an analytical solution. Based on the size of the fracture process zone and its effect on crack extension in ductile rock, the fundamental mechanical difference of LEFM and cohesive fracture mechanics-based methods is discussed. An effective fracture toughness method has been proposed to consider the fracture process zone effect on the ductile rock fracture.     

川东北宣汉-达县地区构造应力场对裂缝的控制

川东北宣汉-达县地区晚白垩世受到南东方向的挤压作用,始新世晚期-渐新世早期受到北东方向的挤压作用,两期构造活动导致宣汉-达县地区下三叠统飞仙关组碳酸盐岩中形成构造裂缝,对油气藏开发产生较大的影响。在考虑岩层与岩层之间相互影响的基础上,结合共轭节理和机械双晶的分析结果,利用三维有限元分析技术,计算宣汉-达县地区飞仙关组古构造应力大小,获得了两期古构造应力场的分布特征。通过岩石破裂阈值的限定,对普光、毛坝区块构造裂缝（张裂缝和剪裂缝）的发育区域进行预测,依据综合破裂率对岩层破裂强度进行评价,为提高裂缝钻遇率,降低勘探开发风险提供了科学的地质依据。      

Detecting the footprint of a longwall mine panel claimed to infringe on a permit boundary at the Soma–Darkale coalfield (Manisa, Turkey) using surface fractures and microgravity measurements

A coal mine panel claimed to infringe on a permit boundary, or to create an hazard after subsidence has been the subject of lawsuits. We study at the Soma–Darkale coalfield (Manisa, Turkey), the footprint of a lignite coal mine panel at a depth of about 150–200 m by mapping all of the surface fractures we could observe, and by developing a post-subsidence density model that we verified through gravity measurements with positive Bouguer anomaly. With the analysis of the fracture map and the gravity data, we were able to identify the footprint of a mine panel from the effect of the anomalous mass due to denser overburden material filling up the space after the extraction of less-dense lignite. Whereas, using empirical methods like the so-called “limit line approach” to evaluate the extent of the area where mining can have subsidence-induced surface fracturing, one could not recognize for certain infringement of permit boundaries. The orientations of the fractures we mapped at the ground surface, the Bouguer gravity map, and a test borehole indicated the presence and dimensions of a coal panel in dispute. The presented approach based on gravity method and fracture observations may be an example to help settle conflicts related to the position of the longwall mine panel.     

Coping with uncertainties through an automated workflow for 3D reservoir modelling of carbonate reservoirs

Reliable 3D modelling of underground hydrocarbon reservoirs is a challenging task due to the complexity of the underground geological formations and to the availability of different types of data that are typically affected by uncertainties.In the case of geologically complex depositional environments,such as fractured hydrocarbon reservoirs,the uncertainties involved in the modelling process demand accurate analysis and quantification in order to provide a reliable confidence range of volumetric estimations.In the present work,we used a 3D model of a fractured carbonate reservoir and populated it with different lithological and petrophysical properties.The available dataset also included a discrete fracture network(DFN)property that was used to model the fracture distribution.Uncertainties affecting lithological facies,their geometry and absolute positions(related to the fault system),fracture distribution and petrophysical properties were accounted for.We included all different types of uncertainties in an automated approach using tools available in today's modelling software packages and combining all the uncertain input parameters in a series of statistically representative geological realizations.In particular,we defined a specific workflow for the definition of the absolute permeability according to an equivalent,single porosity approach,taking into account the contribution of both the matrix and the fracture system.The results of the analyses were transferred into a 3D numerical fluid-dynamic simulator to evaluate the propagation of the uncertainties associated to the input data down to the final results,and to assess the dynamic response of the reservoir following a selected development plan.The"integrated approach"presented in this paper can be useful for all technicians involved in the construction and validation of 3D numerical models of hydrocarbon-bearing reservoirs and can potentially become part of the educational training for young geo-scientists and engineers,since an integrated and well-constructed workflow is the backbone of any reservoir study.     

Numerical simulation of particle plugging in hydraulic fracture by element partition method

Hydraulic fracturing (HF) treatment often involves particle migration and is applied for propping or plugging fractures. Particle migration behaviors, e.g., bridging, packing, and plugging, significantly affect the HF process. Hence, it is crucial to effectively simulate particle migration. In this study, a new numerical approach is developed based on a coupled element partition method (EPM). The EPM is used to model natural and hydraulic fractures, in which a fracture is allowed to propagate across an element, thereby avoiding remeshing in fracture simulations. To characterize the water flow process in a fracture, a fully hydromechanical coupled equation is adopted in the EPM. To model particle transportation in fractures with water flow, each particle is treated as a discrete element. The particles move in the fracture as a result of being dragged by fluid. Their movement, contact, and packing behaviors are simulated using the discrete element method. To reflect the plugging effect, an equivalent aperture approach is proposed. Using this method, the particle migration and its effect on water flow are well simulated. The simulation results show that this method can effectively reproduce particle bridging, plugging, and unblocking in a hydraulic fracture. Furthermore, it is demonstrated that particle plugging significantly affects water flow in a fracture and hence the propagation of hydraulic fracture. This method provides a simple and feasible approach for the simulation of particle migration in a hydraulic fracture.     

An enhanced stochastic optimization in fracture network modelling conditional on seismic events

This paper presents an approach to modelling fracture networks in hot dry rock geothermal reservoirs. A detailed understanding of the fracture network within a geothermal reservoir is critically important for assessments of reservoir potential and optimal production design. One important step in fracture network modelling is to estimate the fracture density and the fracture geometries, particularly the size and orientation of fractures. As fracture networks in these reservoirs can never be directly observed there is significant uncertainty about their true nature and the only feasible approach to modelling is a stochastic one. We propose a global optimization approach using simulated annealing which is an extension of our previous work. The fracture model consists of a number of individual fractures represented by ellipses passing through the micro-seismic points detected during the fracture stimulation process, i.e. the fracture model is conditioned on the seismic points. The distances of the seismic points from fitted fracture planes (ellipses) are, therefore, important in assessing the goodness-of-fit of the model. Our aims in the proposed approach are to formulate an appropriate objective function for the optimal fitting of a set of fracture planes to the micro-seismic data and to derive an efficient modification scheme to update the model parameters. The proposed objective function consists of three components: orthogonal projection distances of the seismic points from the nearest fitted fractures, the amount of fracturing (fitted fracture areas) and the volumes of the convex hull of the associated points of fitted fractures. The functions used in the model update scheme allow the model to achieve an acceptable fit to the points and to converge to acceptable fitted fracture sizes. These functions include two groups of proposals: one for updating fracture parameters and the other for determining the size of the fracture network. To increase the efficiency of the optimization, a spatial clustering approach, the Distance-Directional Transform, was developed to generate parameters for newly proposed fractures. A simulated dataset was used as an example to evaluate our approach and we compared the results to those derived using our previously published algorithm on a real dataset from the Habanero geothermal field in the Cooper Basin, South Australia. In a real application, such as the Habanero dataset, it is difficult to determine definitively which algorithm performs better due to the many uncertainties but the number of association points, the number of final fractures and the error are three important factors that quantify the effectiveness of our algorithm.     

岩石力学参数对裂缝发育程度的影响

弹性模量(E)、泊松比(μ)及密度(ρ)是岩石的重要力学参数, 当其他条件一致时, 在一定程度上影响着裂缝的发育。以塔里木盆地某气田为研究区, 在造缝期古应力场分析的基础上, 利用储层裂缝数值模拟技术, 计算得到储层裂缝孔隙度; 再以裂缝孔隙度为指标, 分析岩石力学参数对裂缝发育程度的影响。研究结果表明, 裂缝孔隙度随弹性模量的增加而增大, 同等应力条件下, 弹性模量越大, 裂缝孔隙度越高, 破裂程度越大; 泊松比小于0.2时, 裂缝孔隙度随泊松比增加而逐渐下降; 泊松比超过0.2后, 裂缝孔隙度随泊松比增加而逐渐增大; 岩石密度对裂缝孔隙度的影响不大, 基本上可以忽略。      

一种计算断裂信息维的方法及其应用

对断裂数据化处理,得到断裂控制点。以断裂控制点为约束,对断裂进行点插值,以单个统计单元为视窗,统计落入不同栅格内的插值点数目,进而求得插值点落入不同栅格的概率,对变量数据拟合,得到断裂信息维以及相关系数。将该思路应用在金湖凹陷阜二段断裂分形评价中,分别计算了断裂长度信息维、面积信息维。结果表明,90%以上的统计单元相关系数0.9,断裂发育区具有较高的自相似性,断裂总体分形特征曲线的相关系数0.999。金湖凹陷断裂的计算表明,该思路是测量断裂信息维的有效方法,能够提高工作效率,具有较好的应用前景。     

基于CT-CA的天然裂隙岩石受拉破坏特性研究

岩石内部存在的裂隙、孔洞等天然损伤对岩石的力学性能和破坏过程有重要影响,依据细胞自动机理论结合CT无损识别技术实现了含天然裂隙岩石在劈裂条件下裂纹扩展和贯通全过程及其力学性能变化规律的研究。从裂隙砂岩的真实细观结构出发,构建了天然裂隙岩石的数值计算模型,运用CASRock数值计算软件完成了含不同裂隙倾角的砂岩劈裂破坏的数值试验,分析了裂隙倾角对砂岩的力学特性、裂纹扩展过程及能量演化的影响规律。研究表明：(1)天然裂隙砂岩的抗拉强度与裂隙倾角密切相关,随着裂隙倾角的增加,其抗拉强度呈现先减小后增加的趋势;(2)裂隙起裂于天然裂隙尖端,当裂隙倾角0°≤θ<48°时,岩样的破坏是由错开型裂纹引起,裂纹沿着与天然裂隙近垂直方向扩展;当裂隙倾角48°≤θ<94°时,岩样的破坏是由张开型裂纹引起,裂纹沿着与天然裂隙近平行方向扩展;(3)劈裂过程中裂纹尖端应力场存在拉应力区和压应力区,拉应力造成翼裂纹由天然裂隙尖端沿加载端方向萌生扩展,而压应力则引发次生裂纹沿天然裂隙方向扩展;(4)含天然裂隙砂岩劈裂破坏过程能量演化可划分为4个阶段,随裂隙倾角的增大,峰值点处的总能量密度、弹性能密度先缓...     

A Spatial Clustering Approach for Stochastic Fracture Network Modelling

Fracture network modelling plays an important role in many application areas in which the behaviour of a rock mass is of interest. These areas include mining, civil, petroleum, water and environmental engineering and geothermal systems modelling. The aim is to model the fractured rock to assess fluid flow or the stability of rock blocks. One important step in fracture network modelling is to estimate the number of fractures and the properties of individual fractures such as their size and orientation. Due to the lack of data and the complexity of the problem, there are significant uncertainties associated with fracture network modelling in practice. Our primary interest is the modelling of fracture networks in geothermal systems and, in this paper, we propose a general stochastic approach to fracture network modelling for this application. We focus on using the seismic point cloud detected during the fracture stimulation of a hot dry rock reservoir to create an enhanced geothermal system; these seismic points are the conditioning data in the modelling process. The seismic points can be used to estimate the geographical extent of the reservoir, the amount of fracturing and the detailed geometries of fractures within the reservoir. The objective is to determine a fracture model from the conditioning data by minimizing the sum of the distances of the points from the fitted fracture model. Fractures are represented as line segments connecting two points in two-dimensional applications or as ellipses in three-dimensional (3D) cases. The novelty of our model is twofold: (1) it comprises a comprehensive fracture modification scheme based on simulated annealing and (2) it introduces new spatial approaches, a goodness-of-fit measure for the fitted fracture model, a measure for fracture similarity and a clustering technique for proposing a locally optimal solution for  fracture parameters. We use a simulated dataset to demonstrate the application of the proposed approach followed by a real 3D case study of the Habanero reservoir in the Cooper Basin, Australia.     

Uniform asymptotic Green's functions for efficient modeling of cracks in elastic layers with relative shear deformation controlled by linear springs

We present a uniform asymptotic solution (UAS) for a displacement discontinuity (DD) that lies within the middle layer of a three‐layer elastic medium in which relative shear deformation between parallel interfaces is controlled by linear springs. The DD is assumed to be normal to the two interfaces between the elastic media. Using the Fourier transform method we construct a leading term in the asymptotic expansion for the spectral coefficient functions for a DD in a three‐layer‐spring medium. Although a closed‐form solution will require a solution in terms of an infinite series, we demonstrate how this UAS can be used to construct highly efficient and accurate solutions even in the case in which the DD actually touches the interface. We compare the results using the Green's function UAS solution for a crack crossing a soft interface with results obtained using a multi‐layer boundary element method. We also present results from an implementation of the UAS Green's function approach in a pseudo‐3D hydraulic fracturing simulator to analyze the effect of interface shear deformation on the fracture propagation process. These results are compared with field measurements. Copyright © 2008 John Wiley & Sons, Ltd.     

On the risk of hydraulic fracturing in CO2 geological storage

We present a contribution on the risk of hydraulic fracturing in CO₂ geological storage using an analytical model of hydraulic fracturing in weak formations. The work is based on a Mohr–Coulomb dislocation model that is extended to account for material with fracture toughness. The complete slip process that is distributed around the crack tip is replaced by superdislocations that are placed in the effective centers. The analytical model enables the identification of a dominant parameter, which defines the regimes of brittle to ductile propagation and the limit at which a mode‐1 fracture cannot advance. We examine also how the corrosive effect of CO₂ on rock strength may affect hydraulic fracture propagation. We found that a hydraulically induced vertical fracture from CO₂ injection is more likely to propagate horizontally than vertically, remaining contained in the storage zone. The horizontal fracture propagation will have a positive effect on the injectivity and storage capacity of the formation. The containment in the vertical direction will mitigate the risk of fracturing and migration of CO₂ to upper layers and back to the atmosphere. Although the corrosive effect of CO₂ is expected to decrease the rock toughness and the resistance to fracturing, the overall decrease of rock strength promotes ductile behavior with the energy dissipated in plastic deformation and hence mitigates the mode‐1 fracture propagation. Copyright © 2016 John Wiley & Sons, Ltd.     

A stabilized extended finite element framework for hydraulic fracturing simulations

We present a stabilized extended finite element formulation to simulate the hydraulic fracturing process in an elasto‐plastic medium. The fracture propagation process is governed by a cohesive fracture model, where a trilinear traction‐separation law is used to describe normal contact, cohesion and strength softening on the fracture face. Fluid flow inside the fracture channel is governed by the lubrication equation, and the flow rate is related to the fluid pressure gradient by the ‘cubic’ law. Fluid leak off happens only in the normal direction and is assumed to be governed by the Carter's leak‐off model. We propose a ‘local’ U‐P (displacement‐pressure) formulation to discretize the fluid‐solid coupled system, where volume shape functions are used to interpolate the fluid pressure field on the fracture face. The ‘local’ U‐P approach is compatible with the extended finite element framework, and a separate mesh is not required to describe the fluid flow. The coupled system of equations is solved iteratively by the standard Newton‐Raphson method. We identify instability issues associated with the fluid flow inside the fracture channel, and use the polynomial pressure projection method to reduce the pressure oscillations resulting from the instability. Numerical examples demonstrate that the proposed framework is effective in modeling 3D hydraulic fracture propagation. Copyright © 2016 John Wiley & Sons, Ltd.     

Numerical simulation of fracture flow with a mixed-hybrid FEM stochastic discrete fracture network model

We introduce a discrete fracture network model of stationary Darcy flow in fractured rocks. We approximate the fractures by a network of planar circle disks, which is generated on the basis of statistical data obtained from field measurements. We then discretize this network into a mesh consisting of triangular elements placed in three-dimensional space. We use geometrical approximations in fracture planes, which allow for a significant simplification of the final triangular meshes. We consider two-dimensional Darcy flow in each fracture. In order to accurately simulate the channeling effect, we assign to each triangle an aperture defining its hydraulic permeability. For the discretization we use the lowest order Raviart-Thomas mixed finite element method. This method gives quite an accurate velocity field, which is computed directly and which satisfies the mass balance on each triangular element. We demonstrate the use of this method on a model problem with a known analytical solution and describe the generation and triangulation of the fracture network and the computation of fracture flow for a particular real situation.     

Modeling non-Darcy flows in realistic pore-scale proppant geometries

The ability to evaluate the effective permeability of proppant packs is useful in predicting the efficiency of hydraulic fracture installations. In this paper we propose a computational approach combining microimaging data from X-ray computed microtomography, the simulations of flow at pore-scale, and an upscaling process which identifies the effective model parameters at the core-scale. With this computational approach applied to proppant pack we confirm the reduction in the fracture conductivity and subsequent reduction in the productivity of a hydraulically fractured reservoir due to the high flow rates and to the migration of fine particles resulting in pore throat bridging.     

岩质高边坡卸荷带形成及其工程性状研究

首先针对边坡开挖或河谷下切的卸荷过程, 讨论了边坡应力场的分布, 提出了边坡二次应力的驼峰应力分布规律。在此基础上, 分析了伴随边坡二次应力场的形成, 岩质高边坡卸荷带的形成机理。进-步, 结合三峡船闸高边坡的开挖和监测实践, 讨论了卸荷带的工程地质意义及其力学性状表现。最后, 利用本文的基本观点, 对三峡船闸高边坡卸荷带进行了合理的数值模拟研究。     

渤中凹陷断裂成因类型及其对成藏的控制作用

在对渤中凹陷进行大量精细地震解释基础上,按照断层的发育过程,将渤中凹陷古近系—新近系的断裂划分为消亡型、继承型、继承-改造型和新生型。结合目前所发现的油气藏分布特点,确定不同类型断裂对油气的运移和成藏具有不同的控制作用。消亡型断裂是由早期伸展作用而成的正断层,古近纪发育,新近纪停止活动,与该型断裂有关的油气藏很少;继承型断裂是从古近纪到新近纪持续受伸展作用形成的正断裂,因长期活动,该型断裂以垂向输导油气为主,以油气成藏为辅;继承-改造型断裂在古近纪受控于伸展作用,而在新近纪受控于剪切作用,该型断裂不但有利于油气的输导和运移,而且利于油气的成藏;新生型断裂在新近纪时期受强烈的剪切作用所形成,其与继承型或继承-改造型断裂相伴生时较有利于成藏。      

岩石破裂过程中电磁辐射信号特征研究

为了探索震前电磁异常现象的物理机制,许多研究注重于分析岩石破裂过程中产生的电磁辐射信号。对花岗岩样品进行单轴加载,变形直至破裂,记录整个过程中产生的电磁辐射(EME)和声发射(AE)信号,对比分析。这里主要从两个方面分析岩石破裂过程中EME信号的特征:①利用非广延分析方法分析EME的能量分布情况,并与b值分析方法对比,推断岩石破裂类型以及裂纹发育过程;②利用统一等待时间定标律分析EME的时间特征,期望获得岩石破裂过程中EME信号等待时间的分布规律。结果表明,在拟合AE和EME信号的能量分布曲线时,发现b值只能拟合AE部分数据,完全不能拟合EME数据,而非广延参数q可以很好地拟合这两类信号。通过对比分析AE和EME信号的等待时间概率密度的分布情况,发现EME信号的集成效果相对较差,可能不满足统一等待时间定标律。